In a classic clip on Americas Funniest Home Videos, a sleeping cat rolls gently off the top of a warm TV set. Ignoring air resistance, calculate the position and velocity of the cat after (a) 0.100 s, (b) 0.200 s, and (c) 0.300 s.

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1 000 m/s2 lasting tor at least 1 ms will cause injury. Suppose; a small child rolls off a bed that is 0.40 m above the floor. If the floor is hardwood, the childs head is brought to rest in approximately 2.0 min. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration. In both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.

A car travels on a straight, level road. (a) Starting from rest, the car is going 44 ft/s (30 mi/h) at the end of 5.0 s. What is the cars average acceleration in ft/s2? (b) In 4.0 more seconds, the car is going 88 ft/s (60 mi/h). What is the cars average acceleration for this time period? (c) The car then slows to 66 ft/s (45 mi/h) in 3.0 s. What is the average acceleration for this time period? (d) What is the overall average acceleration for the total time? (Note these convenient British unit conversions: 60 mi/h = 88 ft/s, 45 mi/h = 66 ft/s, and 30 mi/h = 44 ft/s.)